Skip to main content

Save up to 30% on Elsevier print and eBooks with free shipping. No promo code needed.

Save up to 30% on print and eBooks.

Introduction to Operator Theory and Invariant Subspaces

  • 1st Edition, Volume 42 - October 1, 1988
  • Author: B. Beauzamy
  • Language: English
  • eBook ISBN:
    9 7 8 - 0 - 0 8 - 0 9 6 0 8 9 - 0

This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is… Read more

Introduction to Operator Theory and Invariant Subspaces

Purchase options

LIMITED OFFER

Save 50% on book bundles

Immediately download your ebook while waiting for your print delivery. No promo code is needed.

Institutional subscription on ScienceDirect

Request a sales quote
This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is self-contained, except for a few technical tools, for which precise references are given.Part I starts with finite-dimensional spaces and general spectral theory. But very soon (Chapter III), new material is presented, leading to new directions for research. Open questions are mentioned here. Part II concerns compactness and its applications, not only spectral theory for compact operators (Invariant Subspaces and Lomonossov's Theorem) but also duality between the space of nuclear operators and the space of all operators on a Hilbert space, a result which is seldom presented. Part III contains Algebra Techniques: Gelfand's Theory, and application to Normal Operators. Here again, directions for research are indicated. Part IV deals with analytic functions, and contains a few new developments. A simplified, operator-oriented, version is presented. Part V presents dilations and extensions: Nagy-Foias dilation theory, and the author's work about C1-contractions. Part VI deals with the Invariant Subspace Problem, with positive results and counter-examples.In general, much new material is presented. On the Invariant Subspace Problem, the level of research is reached, both in the positive and negative directions.